SOLUTION: Large reusable bottles cost $4 more than small ones. Eight large bottles cost $24 less than 12 small ones. How much does one small bottles cost?

Algebra ->  Equations -> SOLUTION: Large reusable bottles cost $4 more than small ones. Eight large bottles cost $24 less than 12 small ones. How much does one small bottles cost?      Log On


   



Question 1092655: Large reusable bottles cost $4 more than small ones. Eight large bottles cost $24 less than 12 small ones. How much does one small bottles cost?
Found 3 solutions by addingup, MathLover1, MathTherapy:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
L = S+4
8L = 12S-24 substitute for L:
8(S+4) = 12S-24
8S+32 = 12S-24 add 24 on both sides and subtract 8S on both sides, and you get:
56 = 4S rewrite to get the unknown on the left:
4S = 56
S = 14 this is the cost of a small bottle.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let
large bottles: x
small bottles :y
if large reusable bottles cost $4 more than small ones, we have
x=y%2B4.......eq.1
if 8 large bottles cost $24 less than 12 small ones, we have
8x-24=12y
8x=12y%2B24
x=12y%2F8%2B24%2F8
x=3y%2F2%2B3.........eq.2
from eq.1 and eq.2 we have
y%2B4=3y%2F2%2B3
2y%2B8=3y%2B6
8-6=3y-2y
y=2
find x
x=2%2B4.......eq.1
x=6
large bottle cost: $6
small bottle cost : $2

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Large reusable bottles cost $4 more than small ones. Eight large bottles cost $24 less than 12 small ones. How much does one small bottles cost?
Correct answer: 
I keep asking every day: What are some of these people doing on here? They have no idea what they're doing and just fail to give these people correct answers.
Besides, they make these simple problems so, so COMPLICATED, and yet end up with a WRONG ANSWER still. It's RIDICULOUS!
This is how you solve this!
Let cost of each small bottle be S
The cost of each large bottle = S + 4
We then get: 8(S + 4) = 12S - 24
8S - 12S = - 24 - 32
- 4S = - 56

Can it get ANY SIMPLER than this?